Is there a way to make hand painted designs glow?
Quite simply, use an emission shader.
Longer answer:

Make your drawing, and get it as an image file, preferably black and white. You can use GIMP to edit a scanned drawing. It doesn’t technically matter which is which, but to save yourself a node (and possibly some confusion) you can make the glowing part white and the non-glowing part black.
If possible, use a Principled BSDF shader in your object’s material, and connect the drawing to “Emission Strength,” then set “Emission Color” to the desired value.
If Principled BSDF is not an option, input your drawing as the factor in a Mix Shader node, and hook your regular shader and an Emission BSDF to that Mix Shader. Set the Emission BSDF’s color value as desired.